Hamiltonian Dynamical Systems: History, Theory, and Applications

ISBN-13: 9781461384502 / Angielski / Miękka / 2011 / 385 str.

H. S. Dumas; K. R. Meyer; D. S. Schmidt

Opis

From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Spis treści

History.- The Concept of Elastic Stress in Eighteenth-Century Mechanics: Some Examples from Euler.- Book Two of Radical Principia.- Factoring the Lunar Problem: Geometry, Dynamics, and Algebra in the Lunar Theory from Kepler to Clairaut.- Theory and Applications.- A Limiting Absorption Principle for Separated Dirac Operators with Wigner von Neumann Type Potentials.- Lax Pairs in the Henon-Heiles and Related Families.- Poincaré Compactification of Hamiltonian Polynomial Vector Fields.- Transverse Homoclinic Connections for Geodesic Flows.- A New Proof of Anosov’s Averaging Theorem.- Bifuracation in the Generalized van der Waals Interaction: The Polar Case (M = 0).- Energy Equipartition and Nekhoroshev-Type Estimates for Large Systems.- Suspension of Symplectic Twist Maps by Hamiltonians.- Global Structural Stability of Planar Hamiltonian Vector Fields.- Analytic Torsion, Flows and Foliations.- Linearized Dynamics of Symmetric Lagrangian Systems.- A 1:—1 Semisimple Hamiltonian Hopf Bifurcation in Vortex Dynamics.- Stability of Hamiltonian Systems over Exponentially Long Times: The Near-Linear Case.- Constrained Variational Principles and Stability in Hamiltonian Systems.- The Global Phase Structure of the Three Dimensional Isosceles Three Body Problem with Zero Energy.- Non-canonical Transformations of Nonlinear Hamiltonians.- Linear Stability Analysis of Some Symmetrical Classes of Relative Equilibria.- Identical Maslov Indices from Different Symplectic Structures.- Discretization of Autonomous Systems and Rapid Forcing.- Computing the Motion of the Moon Accurately.- On the Rapidly Forced Pendulum.- Existence of Invariant Tori for Certain Non-Symplectic Diffeomorphisms.